The Meaning of 'Symmetry'

There are a lot of discussions of 'symmetry' that give examples and a rather vague definition, but don't make clear why some things aren't 'symmetries' but which seem like they ought to be, at least under the vague definition. My aim here is to give a more precise definition, and show how it applies.

Here I'll just talk about symmetry of figures in the Euclidean plane, since places that give more sophisticated examples usually give a more sophisticated definition as well. Read more about The Meaning of 'Symmetry'

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